# Dynamical entropy of a non-commutative version of the phase doubling

Banach Center Publications (1998)

- Volume: 43, Issue: 1, page 31-40
- ISSN: 0137-6934

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topAndries, Johan, and De Cock, Mieke. "Dynamical entropy of a non-commutative version of the phase doubling." Banach Center Publications 43.1 (1998): 31-40. <http://eudml.org/doc/208852>.

@article{Andries1998,

abstract = {A quantum dynamical system, mimicking the classical phase doubling map $z ↦ z^2$ on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.},

author = {Andries, Johan, De Cock, Mieke},

journal = {Banach Center Publications},

keywords = {quantum dynamical entropy; Lyapunov exponent; ergodicity; noncommutative dynamical entropy; partition of unity},

language = {eng},

number = {1},

pages = {31-40},

title = {Dynamical entropy of a non-commutative version of the phase doubling},

url = {http://eudml.org/doc/208852},

volume = {43},

year = {1998},

}

TY - JOUR

AU - Andries, Johan

AU - De Cock, Mieke

TI - Dynamical entropy of a non-commutative version of the phase doubling

JO - Banach Center Publications

PY - 1998

VL - 43

IS - 1

SP - 31

EP - 40

AB - A quantum dynamical system, mimicking the classical phase doubling map $z ↦ z^2$ on the unit circle, is formulated and its ergodic properties are studied. We prove that the quantum dynamical entropy equals the classical value log2 by using compact perturbations of the identity as operational partitions of unity.

LA - eng

KW - quantum dynamical entropy; Lyapunov exponent; ergodicity; noncommutative dynamical entropy; partition of unity

UR - http://eudml.org/doc/208852

ER -

## References

top- [1] R. Alicki, J. Andries, M. Fannes and P. Tuyls, An algebraic approach to the Kolmogorov-Sinai entropy, Rev. Math. Phys. 8(2) (1996), 167-184. Zbl0884.46039
- [2] R. Alicki and M. Fannes, Defining quantum dynamical entropy, Lett. Math. Phys. 32 (1994), 75-82. Zbl0814.46055
- [3] J. Andries, M. De Cock and M. Fannes, Preprint K.U. Leuven TF-97/29.
- [4] G.G. Emch, H. Narnhofer, G.L. Sewell and W. Thirring, Anosov actions on noncommutative algebras, J. Math. Phys. 35(11) (1994), 5582-5599. Zbl0817.58028
- [5] B. Simon, Trace ideals and their applications, London Mathematical Society Lecture Notes Series 35, Cambridge University Press, Cambridge, 1979. Zbl0423.47001
- [6] P. Tuyls, Towards Quantum Kolmogorov-Sinai Entropy, Ph. D. Thesis, K.U. Leuven, 1997.

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